Décomposition des opérateurs de Riesz et propriétés spectrales de certaines classes de perturbations dans les espaces de Banach riches et exotiques

Abstract

The aim of this thesis is to give a detailed analysis of the spectral properties of certain classes of operators de ned on various types of Banach spaces. Although di¢ cult and extre- mely complicated, the questions that are related are always topical, as the example of West decomposition of Riesz operators and the classi cation of Banach spaces. Here, the characte- rization of polynomially Riesz operators was established on a family of spaces called Smyth Banach spaces, moreover, we give a study of comparison between the maps spectra and Wolf essential spectra of operators de ned on a Banach spaces having rich and poor geometries.